Problem: Simplify the following expression: $ p = \dfrac{7n}{-8n + 9} - 9 $
In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{-8n + 9}{-8n + 9}$ $ \dfrac{9}{1} \times \dfrac{-8n + 9}{-8n + 9} = \dfrac{-72n + 81}{-8n + 9} $ Therefore $ p = \dfrac{7n}{-8n + 9} - \dfrac{-72n + 81}{-8n + 9} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{7n - (-72n + 81) }{-8n + 9} $ Distribute the negative sign: $p = \dfrac{7n + 72n - 81}{-8n + 9}$ $p = \dfrac{79n - 81}{-8n + 9}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{-79n + 81}{8n - 9}$